KöMaL 2012 B4441

The areas of the faces of a tetrahedron are $a$, $b$, $c$, $d$. The angle enclosed by the faces of areas $a$ and $b$ is $\gamma$, the angle of $b$ and $c$is $\alpha$, and the angle of $c$ and $a$ is $\beta$. Prove that $d^2$=$a^2$+$b^2$+$c^2$-2$ab^.$cos $\gamma$-2$bc^.$cos $\alpha$-2$ca^.$cos $\beta$.